Cryptology ePrint Archive: Report 2011/481

Close to Uniform Prime Number Generation With Fewer Random Bits

Pierre-Alain Fouque and Mehdi Tibouchi

Abstract: In this paper we analyze a simple method for generating prime numbers with fewer random bits. Assuming the Extended Riemann Hypothesis, we can prove that our method generates primes according to a distribution that can be made arbitrarily close to uniform. This is unlike the PRIMEINC algorithm studied by Brandt and Damg\aa{a}rd and its many variants implemented in numerous software packages, which reduce the number of random bits used at the price of a distribution easily distinguished from uniform.

Our new method is also no more computationally expensive than the ones in current use, and opens up interesting options for prime number generation in constrained environments.

Category / Keywords: Prime number generation, RSA, efficient implementations, random bits

Date: received 6 Sep 2011

Contact author: mehdi tibouchi at normalesup org

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Version: 20110908:103322 (All versions of this report)

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